Sensitivity analysis from a single input/output sample

The main objective of this paper is to estimate optimally Sobol’ indices at any order when a unique input/output i.i.d. sample is available. Our approach stands on three main ingredients: semi-parametric estimation theory, high-order kernel estimation (inspired by the paper Doksum & Samarov (1995, Ann. Stat., 23, 1443–1473)) and mirror-type transformations as introduced in Bertin et al. (2020, Electron. J. Stat., 14, 2198–2237) and Pujol (2020, arXiv:2205.03199) . We propose two different estimators. We prove that these estimators are asymptotically normal and efficient. Furthermore, we illustrate their numerical properties on standard examples.